21667 ÷ 4 = 5416 R3
Alright, let's work through the division of 21667 by 4 step by step.

Step 1:
4 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 4

Step 2:
4 goes into 21 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 20 from 21 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Step 3:
4 goes into 16 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 54
Subtract 16 from 16 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 4:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 541
Subtract 4 from 6 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 4

Step 5:
4 goes into 27 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 5416
Subtract 24 from 27 to get 3.

The final result is 5416 with a remainder of 3.